sich irren
to be mistaken
To have a false assumption or make a mistake; to be wrong.
Entschuldigung, ich habe mich in der Hausnummer geirrt.
Sorry, I was mistaken about the house number.

to err / wander
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to be mistaken
To have a false assumption or make a mistake; to be wrong.
Entschuldigung, ich habe mich in der Hausnummer geirrt.
Sorry, I was mistaken about the house number.

The verb 'irren' (to err / wander) is closely related to the noun 'der Irrtum' (the error/mistake). When you are mistaken, you make an error.
Sein Glaube, das Projekt sei einfach, war ein großer Irrtum.
His belief that the project was easy was a big mistake.
In the meaning 'sich täuschen' (to be mistaken), 'irren' is always used reflexively. The thing you are mistaken about is often indicated with the preposition 'in' (+ dative).
Ich habe mich im Datum geirrt, das Treffen ist erst morgen.
I was mistaken about the date; the meeting isn't until tomorrow.
The non-reflexive form 'irren' means 'ziellos umherwandern' (to wander aimlessly). This use is rare and rather literary or poetic.
Verloren irrte der Ritter durch den dunklen Wald.
Lost, the knight wandered through the dark forest.
The expression 'Irren ist menschlich' (to err is human) is a fixed proverb. It is used to excuse or put a mistake into perspective.
Keine Sorge wegen des kleinen Fehlers. Irren ist menschlich.
Don't worry about the small mistake. To err is human.
to get lost
'irren' and 'verirren' can both mean that someone is not right or does not find the right way. 'sich irren' is used mostly when you think something false or make a mistake. 'umherirren' can also mean that someone is walking around without a clear goal. 'sich verirren' is more precise when someone loses the way and no longer knows how to reach their destination. Learners confuse the words because both have to do with mistakes or orientation. Practically speaking: for a wrong opinion, you say 'sich irren' (to be mistaken); for a lost route, you say 'sich verirren' (to get lost).

Ich kann mich irren, aber ich glaube, der Kurs beginnt um neun Uhr.
I could be mistaken, but I think the course starts at nine o'clock.
Im großen Krankenhaus hat sich Tom auf dem Weg zur Station verirrt.
In the large hospital, Tom got lost on the way to the ward.